XCSP 2.1 Benchmark Database

Instance: normalized-langford-3-20-ext
Number of variables: 60
Number of constraints: 1770
Satisfiable: True
Timestamp: 2025-07-27 21:34:59
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 60
Number of constraints: 1770

General features

Coarse blocks: 211,480
Value tables: 60

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Arity 2 2 2.00 2.00 3,540 MAX VALUE 1,226.87 0.00 0.00 0.00

Coarse blocks size 1 59 57.94 59.00 12,252,300 MAX VALUE 846,497.00 7.78 0.13 0.09

Relational linkage 0.02 0.02 0.02 0.02 44.67 0.00 -10,972.80 0.00 0.00 0.00

Tightness 0.02 0.99 0.04 0.02 68.29 0.00 -7,083.76 0.14 3.74 0.18

Tuples 39 3,540 3,461.10 3,540.00 6,126,140 MAX VALUE 14,292.30 518.91 0.15 0.18

Values 60 60 60.00 60.00 3,600 MAX VALUE 245.66 0.00 0.00 0.00

Value table constraints 59 59 59.00 59.00 3,540 MAX VALUE 244.65 0.00 0.00 0.00

Value table partitions 60 60 60.00 60.00 3,600 MAX VALUE 245.66 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	3,540	MAX VALUE	1,226.87	0.00	0.00	0.00
Coarse blocks size	1	59	57.94	59.00	12,252,300	MAX VALUE	846,497.00	7.78	0.13	0.09
Relational linkage	0.02	0.02	0.02	0.02	44.67	0.00	-10,972.80	0.00	0.00	0.00
Tightness	0.02	0.99	0.04	0.02	68.29	0.00	-7,083.76	0.14	3.74	0.18
Tuples	39	3,540	3,461.10	3,540.00	6,126,140	MAX VALUE	14,292.30	518.91	0.15	0.18
Values	60	60	60.00	60.00	3,600	MAX VALUE	245.66	0.00	0.00	0.00
Value table constraints	59	59	59.00	59.00	3,540	MAX VALUE	244.65	0.00	0.00	0.00
Value table partitions	60	60	60.00	60.00	3,600	MAX VALUE	245.66	0.00	0.00	0.00

Tree decomposition

Number of clusters: 1
Number of leaves: 1
Tree depth: 0
CIR: None
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Tree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 1,770 1,770 1,770.00 1,770.00 1,770 1,770 7.48 0.00 0.00 0.00

Variables per cluster 60 60 60.00 60.00 60 60 4.09 0.00 0.00 0.00

Separator constraints 0 0 0.00 0.00 0 0 None 0.00 None 0.00

Separator variables 0 0 0.00 0.00 0 0 None 0.00 None 0.00

Clusters per var 1 1 1.00 1.00 60 1 0.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	COV
Cluster constraints	1,770	1,770	1,770.00	1,770.00	1,770	1,770	7.48	0.00
Variables per cluster	60	60	60.00	60.00	60	60	4.09	0.00
Separator constraints	0	0	0.00	0.00	0	0	None	None
Separator variables	0	0	0.00	0.00	0	0	None	None
Clusters per var	1	1	1.00	1.00	60	1	0.00	0.00

Dual tree decomposition

Number of clusters: 58
Number of leaves: 30
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/DualTree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 3,480 44,160 8,438.00 3,480.00 489,404 MAX VALUE 505.82 8,711.85 1.03 1.31

Variables per cluster 117 1,152 260.45 117.00 15,106 MAX VALUE 307.17 235.34 0.90 1.31

Separator constraints 0 25,984 6,668.00 3,364.00 386,744 0 None 5,280.20 0.79 1.31

Separator variables 0 896 229.93 116.00 13,336 0 None 182.08 0.79 1.31

Clusters per variable 1 10 8.53 9.00 15,106 MAX VALUE 3,703.57 2.04 0.24 1.51

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3,480	44,160	8,438.00	3,480.00	489,404	MAX VALUE	505.82	8,711.85	1.03	1.31
Variables per cluster	117	1,152	260.45	117.00	15,106	MAX VALUE	307.17	235.34	0.90	1.31
Separator constraints	0	25,984	6,668.00	3,364.00	386,744	0	None	5,280.20	0.79	1.31
Separator variables	0	896	229.93	116.00	13,336	0	None	182.08	0.79	1.31
Clusters per variable	1	10	8.53	9.00	15,106	MAX VALUE	3,703.57	2.04	0.24	1.51

Primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 34,220
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Primal1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 1.00 1.00 1.00 1.00 60.00 1.00 0.00 0.00 0.00 0.00

Degree 59 59 59.00 59.00 3,540 MAX VALUE 244.65 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 60 1 0.00 0.00 0.00 0.00

MCB cycle size None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	60.00	1.00	0.00	0.00	0.00	0.00
Degree	59	59	59.00	59.00	3,540	MAX VALUE	244.65	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	60	1	0.00	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 34,220

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 1.00 1.00 1.00 1.00 60.00 1.00 0.00 0.00 0.00 0.00

Degree 59 59 59.00 59.00 3,540 MAX VALUE 244.65 0.00 0.00 0.00

Eccentricity 1 1 1.00 1.00 60 1 0.00 0.00 0.00 0.00

MCB cycle size None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	1.00	1.00	1.00	1.00	60.00	1.00	0.00	0.00	0.00	0.00
Degree	59	59	59.00	59.00	3,540	MAX VALUE	244.65	0.00	0.00	0.00
Eccentricity	1	1	1.00	1.00	60	1	0.00	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: None%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Dual1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

Eccentricity None None None None None None None None None None

MCB cycle size None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Minimal dual graph

Density: 0.22%
MCB compute time (ms): None
MCB cycles: None

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.01 25.22 0.01

Degree 2 7 3.93 4.00 6,960 MAX VALUE 2,371.09 0.99 0.25 1.27

Eccentricity 12 22 16.24 16.00 28,742 MAX VALUE 4,922.61 1.84 0.11 1.99

MCB cycle size None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.01	25.22	0.01
Degree	2	7	3.93	4.00	6,960	MAX VALUE	2,371.09	0.99	0.25	1.27
Eccentricity	12	22	16.24	16.00	28,742	MAX VALUE	4,922.61	1.84	0.11	1.99
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated dual graph

Density: None%
Triangles: None

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 4.63%

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.47 1.00 0.82 0.79 1,446.96 0.00 -386.93 0.15 0.18 4.37

Degree 2 421 81.96 9.00 145,076 MAX VALUE 5,139.37 130.59 1.59 4.04

Eccentricity 4 6 4.74 5.00 8,382 MAX VALUE 2,740.03 0.56 0.12 0.83

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.82	0.79	1,446.96	0.00	-386.93	0.15	0.18	4.37
Degree	2	421	81.96	9.00	145,076	MAX VALUE	5,139.37	130.59	1.59	4.04
Eccentricity	4	6	4.74	5.00	8,382	MAX VALUE	2,740.03	0.56	0.12	0.83

Incidence graph

Density: 0.21%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-20-ext/Incidence1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 59 3.87 2.00 7,080 MAX VALUE 1,471.52 10.15 2.62 0.14

Eccentricity 3 4 3.97 4.00 7,260 MAX VALUE 2,519.66 0.18 0.04 0.14

MCB cycle size None None None None None None None None None None

XCSP 2.1 Benchmarks